Very very beautiful

Algebra Level 5

Consider the equation \[ (x+y)^2=(x+1)(y-1)\]

If all the possible real ordered pairs \((x,y)\) that satisfy the equation above are \((x_1,y_1),(x_2,y_2),...,(x_n,y_n)\) then find the value of \(x^2_1+...+x^2_n+y^2_1+...+y^2_n\).

  • If you think there are infinite solutions then answer 777 and if you think no real solutions answer 666.
  • Ordered pair means (11,12),(12,11) are considered different.

This is a part of the set Beautiful..It is!!


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